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Hald, Anders

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935

Hald, Anders - A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935, ebook

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ISBN: 9780387464091
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Table of contents

1. The Three Revolutions in Parametric Statistical Inference

Part I. Binomial Statistical Inference

2. James Bernoulli’s Law of Large Numbers for the Binomial, 1713, and Its Generalization

3. De Moivre’s Normal Approximation to the Binomial, 1733, and Its Generalization

4. Bayes’s Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764

Part II. Statistical Inference by Inverse Probability

5. Laplace’s Theory of Inverse Probability, 1774–1786

6. A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750–1805

7. Gauss’s Derivation of the Normal Distribution and the Method of Least Squares, 1809

8. Credibility and Confidence Intervals by Laplace and Gauss

9. The Multivariate Posterior Distribution

10. Edgeworth’s Genuine Inverse Method and the Equivalence of Inverse and Direct Probability in Large Samples, 1908 and 1909

11. Criticisms of Inverse Probability

Part III. The Central Limit Theorem and Linear Minimum Variance Estimation by Laplace and Gauss

12. Laplace’s Central Limit Theorem and Linear Minimum Variance Estimation

13. Gauss’s Theory of Linear Minimum Variance Estimation

Part IV. Error Theory. Skew Distributions. Correlation. Sampling Distributions

14. The Development of a Frequentist Error Theory

15. Skew Distributions and the Method of Moments

16. Normal Correlation and Regression

17. Sampling Distributions Under Normality, 1876–1908

Part V. The Fisherian Revolution, 1912–1935

18. Fisher’s Early Papers, 1912–1921

19. The Revolutionary Paper, 1922

20. Studentization, the F Distribution, and the Analysis of Variance, 1922–1925

21. The Likelihood Function, Ancillarity, and Conditional Inference

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Keywords: MATHEMATICS / General MAT000000

Author(s)
Publisher
Springer
Publication year
2007
Language
en
Edition
1
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9780387464091

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